... that¹

Note: The Problem was discussed at length at the Math Circle Workshop on June 6th 1998 in Lawrence Hall of Science. Let's see if anyone remembers the beautiful solution we saw there! Now, imagine you are in 7-8th grade, and you haven't yet heard of ``trigonometry'' (oops, that's a hint for the advanced! :-)), and your whole world of geometric tricks consists of similar and congruent triangles, and, say, you know that the sum of angles in a triangle is $180^{\circ}$. Can you do with? Play with it and see how far you can get. Solutions to this Problem 1 and Problem 2 will be handed after the talk.

... Assignment.)²

Warning: Don't try this at home unless you really know what you are doing! This problem is really hard. When you see the solution you will be surprised that it doesn't require any advanced mathematical tools; BUT how one can come up with such a solution - that where the mystery is! So, good luck. :-)